Problem I Let f : R3 -> R be given by the formula Let f : R3 -> R be the function given by the formula - 2x2 + 3y2 + 4xyz + 5x + 6y. Find the critical points and decide whether f has maxima, minima or saddles at them. Problem 2 A fluid is flowing through space with velocity function F : R3 - R given by the formula -([:]) - [2:] The origin is at the exact center of the planet Krypton, which has radius 10000 su- permeters. The state of Supercolorado on the planet Krypton is defined in spherical coordinates by . 0 = " to 0 = 1 . Q = " to 0 = Determine the rate of flow of the fluid through Supercolorado. Problem 3 Consider the function f : R2 -> R given by the formula f ? = xy +xy*+ +3y. Find the quadratic approximation for f at the point a = Problem 4 The surface M is parametrization p : [1, 3] x [1, 5] - R3 given by the formula s+ t 2 = 82 + t rtt